An adaptation reference-point-based multiobjective evolutionary algorithm

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.It is well known that maintaining a good balance between convergence and diversity is crucial to the performance of multiobjective optimization algorithms (MOEAs). However, the Pareto front (PF) of multiobjective optimization problems (MOPs) affects the performance of MOEAs, especially reference point-based ones. This paper proposes a reference-point-based adaptive method to study the PF of MOPs according to the candidate solutions of the population. In addition, the proportion and angle function presented selects elites during environmental selection. Compared with five state-of-the-art MOEAs, the proposed algorithm shows highly competitive effectiveness on MOPs with six complex characteristics

Optimistic versus Pessimistic--Optimal Judgemental Bias with Reference Point

This paper develops a model of reference-dependent assessment of subjective beliefs in which loss-averse people optimally choose the expectation as the reference point to balance the current felicity from the optimistic anticipation and the future disappointment from the realisation. The choice of over-optimism or over-pessimism depends on the real chance of success and optimistic decision makers prefer receiving early information. In the portfolio choice problem, pessimistic investors tend to trade conservatively, however, they might trade aggressively if they are sophisticated enough to recognise the biases since low expectation can reduce their fear of loss

Loss aversion with a state-dependent reference point

This study investigates loss aversion when the reference point is a state-dependent random variable. This case describes, for example, a money manager being evaluated relative to a risky benchmark index rather than a fixed target return level. Using a state-dependent structure, prospects are more (less) attractive if they depend positively (negatively) on the reference point. In addition, the structure avoids an inherent aversion to risky prospects and yields no losses when the prospect and the reference point are the same. Related to this, the optimal reference-dependent solution equals the optimal consumption solution (no loss aversion) when the reference point is selected completely endogenously. Given that loss aversion is widespread, we conclude that the reference point generally includes an important exogenously fixed component. For example, the typical investment benchmark index is externally fixed by the investment principal for the duration of the investment mandate. We develop a choice model where adjustment costs cause stickiness relative to an initial exogenous reference point.Reference-dependent preferences, stochastic reference point, loss aversion, disappointment theory, regret theory.

Pairwise MRF Calibration by Perturbation of the Bethe Reference Point

We investigate different ways of generating approximate solutions to the pairwise Markov random field (MRF) selection problem. We focus mainly on the inverse Ising problem, but discuss also the somewhat related inverse Gaussian problem because both types of MRF are suitable for inference tasks with the belief propagation algorithm (BP) under certain conditions. Our approach consists in to take a Bethe mean-field solution obtained with a maximum spanning tree (MST) of pairwise mutual information, referred to as the \emph{Bethe reference point}, for further perturbation procedures. We consider three different ways following this idea: in the first one, we select and calibrate iteratively the optimal links to be added starting from the Bethe reference point; the second one is based on the observation that the natural gradient can be computed analytically at the Bethe point; in the third one, assuming no local field and using low temperature expansion we develop a dual loop joint model based on a well chosen fundamental cycle basis. We indeed identify a subclass of planar models, which we refer to as \emph{Bethe-dual graph models}, having possibly many loops, but characterized by a singly connected dual factor graph, for which the partition function and the linear response can be computed exactly in respectively O(N) and $O(N^2)$ operations, thanks to a dual weight propagation (DWP) message passing procedure that we set up. When restricted to this subclass of models, the inverse Ising problem being convex, becomes tractable at any temperature. Experimental tests on various datasets with refined $L_0$ or $L_1$ regularization procedures indicate that these approaches may be competitive and useful alternatives to existing ones.Comment: 54 pages, 8 figure. section 5 and refs added in V

Reference point hyperplane trees

Our context of interest is tree-structured exact search in metric spaces. We make the simple observation that, the deeper a data item is within the tree, the higher the probability of that item being excluded from a search. Assuming a fixed and independent probability p of any subtree being excluded at query time, the probability of an individual data item being accessed is (1−p)d for a node at depth d. In a balanced binary tree half of the data will be at the maximum depth of the tree so this effect should be significant and observable. We test this hypothesis with two experiments on partition trees. First, we force a balance by adjusting the partition/exclusion criteria, and compare this with unbalanced trees where the mean data depth is greater. Second, we compare a generic hyperplane tree with a monotone hyperplane tree, where also the mean depth is greater. In both cases the tree with the greater mean data depth performs better in high-dimensional spaces. We then experiment with increasing the mean depth of nodes by using a small, fixed set of reference points to make exclusion decisions over the whole tree, so that almost all of the data resides at the maximum depth. Again this can be seen to reduce the overall cost of indexing. Furthermore, we observe that having already calculated reference point distances for all data, a final filtering can be applied if the distance table is retained. This reduces further the number of distance calculations required, whilst retaining scalability. The final structure can in fact be viewed as a hybrid between a generic hyperplane tree and a LAESA search structure

Reference Point Formation Over Time: A Weighting Function Approach

Although the concept of reference point dependent preferences has been adopted to almost all fields of behavioral economics, especially marketing and behavioral finance, we still know very little about how decision makers form their reference points given a sequence of prices. Our paper provides both a theoretical framework on reference point formation over time, based on cumulative prospect theory’s s-shaped weighting function, and a new experimental method for eliciting subjects’ individual reference points in a finance context. Consistent with our model, we document our subjects’ reference points to be best described by the first and the last price of the time series, with the equally weighted average and the highest price receiving smaller weights.. Results, however, vary strongly on the individual level and are also affected by the elicitation question applied.

Reference Point Dependence for Specification Bias from Quality Upgrading

This paper argues that whether estimates of the welfare cost of natural or artificial trade barriers that do not discriminate by quality are subject to positive or negative specification bias when using models which do not explicitly recognize quality variation depends on the reference point used in counterfactual equilibrium analysis. We use numerical general equilibrium techniques to generate counter examples to the widely held view that (in the competitive case) incorporating quality upgrading will tend to reduce the welfare costs of quality invariant trade barriers. To do this, we use a trade-distorted equilibrium as the reference point, rather than free trade.